Question

Explain how a one-way analysis of variance works. How do you use between-and within-group variability? ** Your answer should indicate that a one-way ANOVA compares the relative size of…..Between-groups variability comes from….while within-groups variability comes from….The F ratio ratio divides….When the I.V. has no effect, the F ratio is about….etc.

Answer 1

One way or two way refers to the number of independent variables in your analysis of variance test.

One way ANOVA has one independent variable with 2 levels. One -way analysis of variance is a technique that can be used to compare means of two or more samples (Using the F-distrubution).

The total variation in the observation Yij can be split into the following two components:

1: The variation between the classes or the variation due to different bases of classification, commonly known as treatments. This variation is known as assignable cause of variation.

2: The variation within the classes , that is inherent variation of the random variable within the observation of a class. This cause of variation is known as chance cause of variation.

In Anova test, we use F test statistic that is the ratio of mean sum of square of between the classes and mean sum of square of within the classes that is the error .

The variance ratio(F) should be calculated only when F>1 otherwise we accept null hypothesis always.